Calculators and tools/Derivatives and Quant

Forward volatility: the volatility priced between two expiries, and the event day inside it.

Two expiries carry two implied volatilities. The volatility the market prices for the days between them follows from total variance, not from an average. Pick a dated pair, check that total variance rises, and see the move an event day would have to carry to account for the gap.

32 dated chains
Total variance check
Event day move

Forward volatility13.72 vol pointsbetween day 15 and day 50
Near and far IV12.83 and 13.46vol points, at the money
Event day move±415 pts1.65% of the index
Ordinary day move±169 pts0.67% of the index

Total variance must not fall. Variance is volatility squared times time. The near expiry holds 0.1283 squared × 0.0411 = 0.00068 and the far expiry 0.1346 squared × 0.1370 = 0.00248. The difference, 0.00181, is the variance the market prices for the 35 days between them, which is a volatility of 13.72 vol points a year. The forward volatility is not an average of the two: it is the one that makes the longer expiry consistent with the shorter.

If one day between the two expiries is an event and the other 34 days run at 12.83 vol points, the ordinary days take 0.00153 of the 0.00181 and the event day is left with 0.00027. That is a one day standard deviation of 1.65%, about ±415 index points, 2.5 times an ordinary day. This is one reading of the prices: the answer depends on the ordinary day volatility, and a day need not be the only place the extra variance sits.

The term structure on 11 Jun 2025 and the volatility priced between each pair of expiries

Solid line: at the money implied volatility of each expiry in the file for the date. Dashed steps: the forward volatility between neighbouring expiries. Source: NSE end of day settlement prices, forward volatility computed by RupeeCase. As of 11 Jun 2025.

Model, not market data

The event day move shifts from 671 to 122 points as the ordinary day volatility is changed by two vol points

Same prices, five assumptions about the quiet days. The answer is a reading of the prices under a model, not a measurement of the event. Inputs: near 12.83 vol points at 15 days, far 13.46 at 50 days, index 25,141, one event day. Source: RupeeCase model on NSE settlement prices. As of 11 Jun 2025.

Total variance by expiry on 11 Jun 2025

Expiry	Days	At the money IV	Total variance	Step from the one before
12 Jun 2025	1	14.11	0.00005	n/a
19 Jun 2025	8	12.02	0.00032	+0.00026
26 Jun 2025	15	12.83	0.00068	+0.00036
31 Jul 2025	50	13.46	0.00248	+0.00180

Implied volatilities are the at the money values of the chains in the file, found by straight line between the two strikes either side of the forward. Time is calendar days over 365. The event day length is one day, and a day counts as one 365th of a year, the same way the engine counts time, so a weekend inside the span is part of the variance. Forward volatility assumes the two implied volatilities are comparable measures of the same index; when they are not, a negative step shows up as a falling total variance. This page cannot trade.

Implied volatilities come from NSE end of day settlement prices, dated on the page. The event move is a reading of prices under a model. Not live, not a forecast, and this page cannot trade.

How to read it

Total variance

Variance is volatility squared times time in years. If the near expiry is priced at 15 vol points for 20 days and the far at 15 for 48, the far expiry holds more total variance simply because it is longer. Total variance must rise with the expiry: if it falls, no volatility between the two can explain it.

Forward volatility

The variance of the span between the expiries is the far total variance less the near one. Dividing by the length of the span and taking the root gives the forward volatility, a yearly figure for those days only. It is not the average of the two implied volatilities.

The event day

Suppose one day in the span is an event and the quiet days run at the volatility you set. The quiet days take their share of the span variance, and what is left is the event day. Its square root times the index is the move it is priced for, in points, beside a quiet day.

How far to trust it

The answer moves with the quiet day volatility, which the chart shows for five choices. The forward volatility module works the arithmetic and the term structure and event variance module covers its use and its limits.

What it leaves out

The implied volatility of each expiry is the at the money one, found by straight line between the two strikes either side of the forward. Weekly and monthly expiries can be priced a little differently, so a pair of mixed types can give a forward volatility that reflects that. One day carries all of the extra variance in the model, which a real event rarely does, and events seldom fall on the dates a chain happens to bracket. The page does not know which events were due; it prices the gap, whatever caused it.

Go to the source

NSE, equity derivatives contract specifications: expiry cycles, lot sizes and cash settlement
NSE, India VIX: what it measures and how it is computed
Gatheral, The Volatility Surface: A Practitioner's Guide, Wiley (2006) book

Is forward volatility a forecast?

No. It is the volatility implied by two prices today for the days between the expiries. It includes the market's price for bearing that risk, so it is not an unbiased estimate of what the index will do.

What if total variance falls between the expiries?

Then no volatility can fit both prices. On a real day it points to a stale quote or an arbitrage; on typed inputs it means the numbers cannot both be right.

Why does the event move depend on the quiet day volatility?

Because the model gives the quiet days their share first. A higher quiet day volatility leaves less for the event day, and a lower one leaves more.

LLearn it in depth

Module 16.9Term structure and event varianceAdvanced, Path 16 Module 16.10Forward volatility from two expiriesAdvanced, Path 16 Module 17.19Event hedging with event varianceAdvanced, Path 17 ToolPayoff builderLegs from a dated chain Pillar guideDerivatives and QuantPaths 12 to 19

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Education only, not investment advice, a research report or a recommendation to buy, sell or hold any security. RupeeCase (QC Alpha Technologies Pvt Ltd) is not registered with SEBI as an investment adviser or research analyst. Contracts and prices shown are for illustration only, come from NSE end of day files at least 30 days old, and are not recommendatory. Derivatives trading carries a high risk of loss.